The invention relates generally to digital data communication systems and more particularly to coding techniques for addressing transmission errors in such systems.
There are basically two approaches to controlling transmission errors in digital data communication systems: automatic repeat request (ARQ) and forward error correction (FEC). Although ARQ schemes offer high system reliability, they also are subject to poor throughput with increasing channel error rates, such as in a wireless communication channel. FEC schemes offer the possibility of constant throughput but with less reliability than ARQ schemes. Various schemes have been proposed which combine the two approaches, typically referred to as “hybrid” ARQ techniques, in which some form of coding technique is utilized at the transmitter and receiver, and decoding errors trigger retransmission requests.
An advantageous coding technique which proves to be very useful when utilized with hybrid ARQ is what is referred to in the art as “rate compatible” coding. Rate compatible codes are a family of nested error correction codes where the codeword bits from higher rate codes are embedded in the lower-rate codes. Thus, a hybrid ARQ scheme can achieve incremental redundancy by having a transmitter send the higher-rate coded bits first and send additional parity bits later if required from the receiver. There are two basic approaches to obtaining rate compatible codes—one is by “puncturing” code bits in a low-rate mother code to obtain a higher rate code; the other is by “extending” a high-rate mother code to lower-rate codes by appending more parity bits. Rate compatible codes were first introduced using puncturing on convolutional codes. See J. Hagenauer, “Rate Compatible Punctured Convolutional Codes (RCPC codes) and their Applications,” IEEE Trans. Commun., Vol. 36, No. 4, pp. 389-400 (April 1988). Recently, attempts have been made to design rate compatible codes for what are known in the art as low density parity check (LDPC) codes. See, e.g., J. Li and K. Narayanan, “Rate-Compatible Low-Density Parity Check Codes for Capacity-Approaching ARQ Schemes in Packet Data Communications,” in Proc. Int. Conf. Commun., Internet, and Inform. Techn. (CIIT) (Nov. 2002). LDPC codes are attractive because they offer good performance while enjoying lower decoding complexity. A puncturing approach for irregular LDPC codes has been proposed which optimizes the degree profiles of an LDPC code ensemble based on density evolution analysis. See J. Ha and S. McLoughlin, “Optimal Puncturing of Irregular Low-Density Parity-Check Codes,” in Proc. IEEE Int. Conf. Commun. (ICC), pp. 3110-14 (May 2003). While showing good puncturing profiles that approach capacity, the results presume an infinite codeword length, which might not be suitable for design of rate compatible LDPC with short block length. Recently, a new puncturing approach has been proposed specifically for finite-length LDPC which is based on grouping nodes with different recoverable steps. See J. Ha and S. McLaughlin, “Puncturing for Finite Length Low-Density Parity-Check Codes,” in Proc. IEEE Int. Symp. Inform. Theory (ISIT), p. 151 (June 2004).